Considerations on Partially Identified Regression Models
41 Pages Posted: 12 Apr 2012 Last revised: 17 Apr 2012
Date Written: March 1, 2012
Motivated by Manski and Tamer (2002) and especially their partial identification analysis of the regression model where one covariate is only interval-measured, we offer several contributions. Manski and Tamer (2002) propose two estimation approaches in this context, focusing on general results. The modified minimum distance (MMD) estimates the true identified set and the modified method of moments (MMM) a superset. Our first contribution is to characterize the true identified set and the superset. Second, we complete and extend the Monte Carlo study of Manski and Tamer (2002). We present benchmark results using the exact functional form for the expectation of the dependent variable conditional on observables to compare with results using its nonparametric estimates, and illustrate the superiority of MMD over MMM. For MMD, we propose a simple shortcut for estimation.
Keywords: partial identification, true identified set, superset, MMD, MMM, estimation
JEL Classification: C01, C13, C40
Suggested Citation: Suggested Citation